An empirical analysis of disability and household expenditure allocations

Transcription

1 An empirical analysis of disability and household expenditure allocations Hong il Yoo School of Economics University of New South Wales

2 Introduction Disability may influence household expenditure allocations in several dimensions Eg loss of earnings potential, constraints on time inputs This study is based on an Engel curve analysis Focus on current expenditure allocation across non-durable goods Model to be estimated is static & covers market goods Empirical applications have been rare Jones and O Donnell (J. Pub Econ, 95) : Compares Engel curves of childless couples w/ disability vs couples w/o disability in a unitary setting

3 Introduction Extend Jones & O Donnell s analysis with benefit from recent advance in demand analysis A collective model due to Lewbel & Pendakur ( 08) In a childless couple household, how does disability of one spouse affect : Intra-household resource allocation between spouses & the extent to which goods are jointly consumed, after taking into account individual-level preference changes due to disability? Very little is known about these issues

4 Overview Primary data source: Canadian Survey of Household Spending Major findings Individual Engel curve estimates show expected responses to disability eg. spend less on clothing, more on hhld ops. Sharing rule is more precisely estimated than economies of scale Variations in total expenditures help identify both But sharing rule has other sources of variations too Own disability reduces woman s share of resources by 3~6 % pts while spousal disability increases it by 4~9% pts. Some estimates suggest that disability reduces benefits from joint consumption but too imprecise to warrant firm conclusions

5 Literature Recent interest in the impact of disability on household consumption from the policy literature Tibble ( 05) and Stapleton et al. ( 08) for extensive reviews Objective is to analyse extra costs of living associated with disability instead of earnings losses Intended to inform disability allowance programs The standard of living approach is gaining popularity Similar concept as equivalence scales in microeconomic demand analysis

6 Literature Disability recognised as an area of application in theoretical contributions eg Lewbel ( 85) and Blackorby & Donaldson ( 92) Empirical applications have been rare Most household expenditure surveys collect no info on disability The only exception?: Jones and O Donnell (J.Pub Eco, 95) Uses a one-off supplement to UK Family Expenditure Survey Focuses on equivalence scales which can be estimated from a single equation regression over a single cross section Compares Engel curves of childless couples w/o disability vs childless couples w/ disability

7 Literature Jones & O Donnell ( 95) ctd. Under certain restrictions on preferences, conclude that a disabled couple needs to spend at least 40~70% more to be as well off as a non-disabled couple A possible interpretation: disability affects the extent to which goods can be jointly consumed within the household The present analysis extends Jones & O Donnell s analysis by incorporating recent advance in demand analysis Estimate a collective Engel curve system previously applied to Canadian data (Lewbel & Pendakur, 08) and 05 Irish data (Bargain et al., 10) (These papers did not incorporate health or disability in the analysis)

8 Motivation Consider person A who may marry a disabled person B or a nondisabled person C What may explain differences in spending patterns of couple {A, B} and couple {A,C}? One simple answer: B s preferences are different from C s Another: structural components of interest Disability may affect jointness of consumption goods and how household resources are shared between spouses

9 Motivation Can we disentangle preference differences from the structural components at least to some extent? Evidence on the economies of scale changes over and above preference changes may provide a strong economic justification for policy intervention Information on changes in resource shares may be relevant for poverty & inequality analysis

10 Modelling framework A collective household demand model of Browning, Chiappori & Lewbel (unpublished; 09) Key features : Intrahousehold resource allocation is Pareto efficient Total consumption of husband & wife > expenditure on goods Due to jointness of consumption Incorporated into the model using Barten-Gorman technology Assume that preferences remain stable before & after marriage ie relevant preference changes can be parametrised independently Combine data on singles and couples to recover sharing rule & economies of scale

11 Empirical specification Given the short span of data, estimate a collective Engel curve system instead of a demand system with price variations Lewbel and Pendakur (J.Econometrics; 08) develops relevant restrictions on preferences Structural in the sense that the sharing rule and the economies of scale parameters are separately identified Model specification consists of three building blocks summarised below

12 Empirical specification Step 1: Specify individual Engel curves incorporating preference changes due to disability (& other demographic controls) These are estimated from data on singles (and couples) Step 2: Construct household Engel curves by combining individual Engel curves according to the theoretical structure Economies of scale and sharing rule functions are introduced into the system Step 3: Parameterise economies of scale & sharing rule The new parameters are estimated from data on couples

13 Step 1: Specifying individual Engel curves First, specify an individual Engel curve system which incorporates preference differences b/w person B and C A parsimonious specification: Introduce demographics including disability into a quadratic Engel curve system using Shape Invariance transformation w a a ' z b (ln y e ' z ) c (ln y e ' z ) k k 0 k k k 2 k i i i i i i i i i i i w ( y, z ) k k i i i k = 1,2,,K goods - i = male, female z i = vector of demographic characteristics including disability ln y = log of expenditure budget

14 Step 2 : Combine individual Engel curves Second, specify a household Engel curve system incorporating the effects of joint consumption and sharing rule : ( Z) y [1 ( Z)] y w k ( Z) w k (, z ) [1 ( Z)] w k (, z ) h f f m m ( z ) ( z ) ln ( z ) ln ( z ) ( Z) f f [1 ( Z)] m m k h ln p ln p Z = z f, z m and distribution factors 0 < η(z) < 1 : female spouse s share of household resources, y 0.5 < δ i (z i ) < 1 : spouse i s benefit from joint consumption p k : price of good k f f m m k k

15 Step 3: Parameterise economies of scale & sharing rule To minimise non-linearities, sharing rule and economies of scale functions are specified to be linear in demographics : ( Z) r r ' Z ln ( z ) d d ' z ln ln ( z ) 0 i i 0i i i i p k i n n ' z k 0 i i i In simple, economies of scale is introduced by taking additional Shape Invariance transformation

16 Empirical specification : An example Given the functional forms, wife s contribution to the household budget share of good k is : 0 k0 k f f f ( r r ' Z)[ a a ' z n n ' z k 0 f f f k f b (ln y e ' z ln( r r' Z) d d ' z ) f f 0 0 f f f k f c (ln y e ' z ln( r r ' Z) d d ' z ) ] f f 0 0 f f f 2 Black : Cross equation restrictions b/w single women & married women Red : Extra terms due to sharing rule & economies of scale

17 Empirical specification The key identifying assumption of this model is that single and married individuals share the same Engel curve parameters in k k w ( y, z ) & w ( y, z ) m m f f Thus joint estimation of singles and couples Engel curve systems allows recovery of the structural components Below, estimation is done by FGNLS on TSP 5.1 Fairly restrictive if singles preferences are fundamentally different from those who choose to marry For robustness checks, restrict the sample of singles to those who have been previously married

18 Empirical specification To sum up, the Engel curve system looks like: w w ( y, z ) k k k f f f f w w ( y, z ) k k k m m m m k k ( y) y k [1 ( y)] y k k wh ( Z) wf (, z f ) [1 ( Z)] wm (, zm) nh ( Z) h ( z ) ( z ) f f m m zi ( agei, educi, worki, disability i ) Z z, z, woman ' s share of household income f m

19 Data : an overview Canadian Survey of Household Spending, Cross sectional recall data on household spending Provides an individual-level disability indicator for the reference person and his/her spouse Defined as presence of physical, mental or health conditions which induce activity limitations Severity index is not provided Key limitation of these data In Jones and O Donnell s ( 95) UK study, severity or type of condition not found to be significant Some informal sensitivity checks have been done using percentiles of total OOP health expenditure

20 Data : sampling choices Basic sampling criteria follow Lewbel and Pendakur ( 08) : To facilitate comparison with the previous study Childless singles and couples reside in large urban areas (minimise effects on home production) aged (minimise labour market entry & exit effects) Live on rented dwellings (rent not observed for home owners) Choice of pooling cross sections time periods Engel curve analysis assumes constant prices Pooling cross sections increase sample size Particularly important as a small fraction of the sample is disabled This presentation focuses on and results

21 Data : sampling choices Total expenditure budget has been deflated by CPI from Statistics Canada An alternative may be to construct a Stone index or use provincial deflators Inflation rate between 04 and 07 has been 6% nationwide 2% b/w 04 and 05 Relative price changes yet to be checked

22 Data : expenditure classification The most disaggregated system to be estimated include 11 categories : 1. Food at home 2. Restaurant meals 3. Recreation goods (eg DVDs, video games) 4. Leisure (eg movie tickets, sports fees) 5. Personal care 6. Household operations 7. Transport 8. Alcohol 9. Clothing 10. Household furnishings & equipment 11. Housing (Rent + energy)

23 Data key features data 2,051 households in total : 1,522 singles couples 667 single women in total : 135 disabled (21%) 845 single men in total : 163 disabled (19%) 529 couples in total: 63 disabled men (12%) & 59 women (11%) data 3,971 households in total : 2,966 singles + 1,008 couples 1,308 single women in total : 292 disabled (22%) 1,658 single men in total : 313 disabled (19%) 1,008 couples in total : 116 disabled men (12%) & 115 women (11%)

24 Data key features It is likely that disabled singles face less severe restrictions than their counterparts in couples on average Given the model specification, the impact on the economies of scale may be contaminated by the impact of severity increase Raw data on budget shares show that spending pattern differences exist between disabled & non-disabled singles though Eg budget share of food at home (restaurant meals) is 0.02 higher (lower) for disabled singles

25 Data mean budget share, singles man_no man_dis fem_no fem_dis food in food out recreation leisure ops pcare transport alcohol housing clothing furneq # obs

26 Data mean budget shares, couples no_dis man_dis fem_dis both_dis food in food out recreation leisure ops pcare transport alcohol housing clothing furneq # obs

27 Estimation strategy 1. Choose the level of disaggregation Here I summarise the results from 11, 9 and 7 category systems To reduce the number of parameters to be estimated Check for robustness to expenditure classifications 2. Start with a full set of demographic characteristics (age, college education, employment & disability). Drop the employment dummy. Drop the education dummy. 3. Check for parametric restrictions which may improve statistical precision of economies of scale estimates Eg restricting slope coefficients across genders

28 Main results woman s resource share The sharing rule is far more precisely estimated than the economies of scale The economies of scale enters the model only as the budget multiplier The sharing rule multiplies the budget AND controls how similar the household Engel curve is to the single woman s Engel curve The magnitude of woman s resource share is closer to Bargain et al. ( 10) s study of Irish couples in 2005 than Lewbel and Pendakur s ( 08) study of Canadian couples from in Bargain et al : Woman s share is somewhere around 0.55 Lewbel and Pendakur: Woman s share is around 0.40 *Browning et al. : Woman s share is over 0.60

29 Main results woman s resource share The reference couple : -Both spouses aged 40 -Both without disability -Both without college education -(Both outside full-time employment) -Wife contributes 40% of the couple s pre-tax income In sample, the reference wife s resource share estimate is a bit above 0.50 in general with t ratios well in excess of 4 Some variations depending on demographic controls 0.52 in 11-goods, 0.50~0.53 in 9-goods and 0.50~0.56 in 7-goods Similar to sample, though there the resource share is a bit below 0.50

30 Main results woman s resource share Wife s resource share increases in her gross income share Precisely estimated at 5% level across all specifications & samples The coefficient estimate is around when employment dummies are controlled, and when excluded Eg for someone otherwise identical to the reference case, changing her income share from 0 to 1 changes her resource share from to Similar in magnitude to findings in Lewbel & Pendakur ( 08)

31 Main results woman s resource share Wife s resource share decreases in own disability and increase in spousal disability In 04 and 05 sample, own disability reduces her resource share by 0.05~0.06 and spousal disability increases it by 0.07~0.09 The point estimates tend to be marginally in/significant at 10% level In 04 and 07 sample, both own (-0.04~-0.05) and spousal disability (0.04~0.06) effects somewhat smaller in magnitude, though they are usually significant at 10% level and occasionally at 5% level Other demographic variations in resource share do not exhibit robust patterns

32 04-05 Woman s resource share, 11 goods Est S.E. Est S.E. Est S.E. intercept ** ** ** fem_shr ** ** ** fem_age man_age fem_work man_work fem_educ man_educ ** fem_dis * * man_dis 0.076* * # parameters # obs. Specification 1 Specification 2 Specification Intercept repreresents woman s resource share in the reference household

33 04-07 Woman s resource share 11 goods Specification 1 Specification 2 Specification 3 Est S.E. Est S.E. Est S.E. intercept ** ** ** fem_shr ** ** * fem_age man_age fem_work man_work ** fem_educ man_educ fem_dis ** * man_dis * * * # parameters # obs

34 Main results economies of scale Economies of scale parameters have been imprecisely estimated in general To be consistent with underlying structural interpretation, the estimated scale must lie between 0.5 (all goods are jointly consumed) and 1 (all goods are privately consumed) For the reference wife, the scale estimate ranges from 0.48 to 0.67 For the reference husband, the scale estimate ranges from 0.41 to 0.74

35 Main results economies of scale The range of the estimates are more similar to Bargain et al. s than Lewbel and Pendakur s The latter authors estimates are around.7 for women and.78 for men Demographic variations, including those along disability, around the reference cases exhibit a fair amount of instability too Contrasts with individual preference deflators ei' z effects of age and disability show up significantly i where the

36 04-05 log scale estimates : 11 goods Specification 1 Specification 2 Specification 3 Est S.E. Est S.E. Est S.E fem_intercept * * ** fem_age ** * ** fem_educ fem_work fem_dis man_intercept * man_age man_educ man_work man_dis # parameters # obs Intercept represent reference person s log scale economy

37 04-07 log scale estimates : 11 goods Specification 1 Specification 2 Specification 3 Est S.E. Est S.E. Est S.E fem_intercept ** ** ** fem_age fem_educ ** fem_work ** fem_dis man_intercept man_age * man_educ 0.753** ** man_work man_dis * ** # parameters # obs

38 Discussion Due to overall instability of the scale estimates, difficult to answer whether differences b/w spending patterns of couples w/ and w/o disability can be partly explained by the economies of scale Along with wife s income share, own and spousal disability are found to influence her share of resources significantly In this study, the effect of disability has been estimated while holding income share constant In practice, own disability may be accompanied by lower earnings Full impact of disability on intra-household resource allocations may be bigger than what the point estimates suggest

39 Extensions? A natural extension may be to concentrate on the issue of intrahousehold resource allocations instead of analysing household economies of scale at the same time Have been recent advance in modeling approaches which facilitate identification of sharing rules in a multi-person household For example Dunbar, Lewbel and Pendakur ( 10) Allows to extend the scope beyond childless couples Doesn t require estimation of a full Engel curve system More robust estimates may be obtained

40 Theoretical framework Due to Browning, Chiappori and Lewbel (unpublished, 09) Assumes that the household behaves as if solving the following program : μ = Pareto weight U f q U m q q, q f m max ( ) ( ) f m s. t. p ' x y and q q Ax qf, qm = individual consumption vectors x = vector of purchased consumption goods A = matrix of household consumption technology f m

41 Theoretical framework Eg if A is a diagonal matrix of the same dimension as x (Barten technology), A k = 1 for pure private goods ie summation of individual consumption of good k equals what has been purchased A k = 2 for pure public goods ie summation of individual consumption is twice what has been purchased 1 < A k < 2 in general k k k k m q q A x f

42 Theoretical framework Provides decentralised duality results eg for a female spouse V y A p q A q y A p f 1 k k k 1 (, ) f f(, ) where V(.,.) is the indirect utility function Thus, the household demand system is given by : x A q y A p A q y A p k k 1 k 1 k 1 k 1 ( ) f(, ) ( ) m([1 ], ) The budget share form of which is : w w y A p w y A p k k 1 k 1 f(, ) [1 ] m([1 ], )

43 Theoretical framework Estimation of a full BCL demand system requires a long span of budget data and is computationally cumbersome Lewbel and Pendakur ( 08) impose the following restriction on preferences to transform the demand system into an Engel curve system : f 1 f y m 1 m [1 ] y V ( y, A p) V (, p) & V ([1 ] y, A p) V (, p) f ie there are budget deflators which can induce the same effect as price deflators m

44 04-05 log scale estimates : 7 goods Specification 1 Specification 2 Specification 3 Est S.E. Est S.E. Est S.E fem_intercept ** ** fem_age ** ** ** fem_educ fem_work fem_dis man_intercept ** man_age man_educ man_work man_dis # parameters # obs